Additional Topics A47A

Topic 6 Rewriting Formulas

The formula for the surface area S of a cone is S = πr2 + πrℓ. Solve the formula for the slant height ℓ.

SOLUTION

S = πr2 + πrℓ Write the formula.

S − πr2 = πr2 − πr2 + πrℓ Subtract πr2 from each side.

r

S − πr2 = πrℓ Simplify.

S − πr2 — πr = πrℓ — πr Divide each side by πr.

S − πr2 — πr = ℓ Simplify.

The rewritten formula is ℓ = S − πr2 —

πr .

Rewriting a Formula

The formula for converting from degrees Fahrenheit F to degrees Celsius C is

C = 5 — 9 (F − 32). Solve the formula for F.

SOLUTION

C = 5 — 9 (F − 32) Write the formula.

9 — 5 ⋅ C = 9 — 5 ⋅ 5 — 9 (F − 32) Multiply each side by 9 — 5 .

9 — 5 C = F − 32 Simplify.

9 — 5 C + 32 = F − 32 + 32 Add 32 to each side.

9 — 5 C + 32 = F Simplify.

The rewritten formula is F = 9 — 5 C + 32.

Rewriting the Temperature Formula

®

1. Temperature The formula K = C + 273.15 converts temperatures from Celsius C to Kelvin K.

(a) Solve the formula for C.

(b) Convert 300 K to Celsius.

2. Interest The formula for simple interest is I = Prt.

(a) Solve the formula for t.

(b) Use the new formula to fi nd the value of t (in years) in the table.

l $75

p $500

r 5%

t

FloridaStandards

Learning StandardMACC.912.A-CED.1.4

Reprinted by permission. Copyright © 2014 Big Ideas Learning, LLC. All rights reserved.

3. Distance The formula for the distance d is d = rt, where r is the rate and t is the time.

(a) Solve the formula for r.

(b) A car travels 180 miles in 3 hours. Use the new formula to fi nd the rate the car is moving.

4. Volume The formula for the volume V of a rectangularpyramid is V = 1 — 3 ℓwh, whereℓis the length of the base, w is the width of the base, and h is the height of the pyramid.

(a) Solve the formula h = 3 in.

w = 2 in.

V = 8 in.3

for ℓ.

(b) Use the new formula to fi nd the length of the base of the rectangular pyramid.

5. Profi t The total profi t P for a company is given by P = R − C, where R is the total revenue and C is the total cost.

(a) Solve the formula for C.

(b) In a year, a company has a total profi t of $68 thousand and a total revenue of $83 thousand. Use the new formula to fi nd the total cost for the company.

6. Perimeter The perimeter P of a rectangle is given by P = 2ℓ + 2w, whereℓis the length and w is the width.

(a) Write the formula for w.

(b) Use the new formula to fi nd the width of the rectangular deck.

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7. Area The formula for the area A of a trapezoid is A = 1 — 2 (b1 + b2)h, where b1 is one base, b2 is the other base, and h is the height.

(a) Solve the formula for b2.

b1 = 7 cm

b2

h = 4 cm

A = 24 cm2 (b) Use the new formula to fi nd the other base of the trapezoid.

8. Surface Area The formula for the surface area S of a right cylinder is S = 2πr(h + r), where r is the radius and h is the height.

(a) Solve the formula for h.

(b) Use the new formula to fi nd the height of the right cylinder.

h

S = 150 m2

r = 3 m

9. Force Newton’s law of gravitation is given by the formula

F = G ( m1m2 —

d2 )

where F is the force between two objects of masses m1 and m2, G is the gravitational constant, and d is the distance between the two objects. Solve the formula for m1.

10. Revenue The total revenue R for a benefi t concert is given by R = Ap1 + Cp2, where A is the number of adult tickets sold, C is the number of child tickets sold, p1 is the price per adult ticket, and p2 is the price per child ticket. Solve the formula for p2.

11. Sale Price The sale price S (in dollars) of an item is given by the formula S = L − rL, where L is the list price (in dollars) and r is the discount rate (in decimal form).

(a) Solve the formula for L.

Sale price:$21

Sale price:$21

(b) The discount rate of the shirt is 30%. Use the new formula to fi nd the list price.

12. Surface Area The formula for the surface area S of a rectangular prism is S = 2ℓw + 2ℓh + 2wh, where ℓis the length, w is the width, and h is the height.

(a) Solve the formula for h.

(b) A rectangular prism has a surface area of 236 square millimeters, a length of 8 millimeters, and a width of 5 millimeters. Use the new formula to fi nd the height.

Additional Topics A47B